To prevent users other than the owner from writing to the USB drive, the 'ro' (read-only) option can be used. This option mounts the filesystem in a read-only mode, allowing only the owner to write to it, thus addressing the administrator's requirement. Other options such as 'rw' (read-write), 'sync', and 'noexec' would not achieve the desired behavior: 'rw' would allow writing by all users, 'sync' would just affect the synchronization timing but not permissions, and 'noexec' would prevent execution of binaries but not affect write permissions.